1. Technical Field
The present invention relates to a quantum state estimation method, a quantum state estimation device and a computer program for estimating a quantum (movement) state of an atom or a molecule adsorbed on a surface of a material, and particularly relates to a quantum state estimation method, a quantum state estimation device and a computer program for realizing the quantum state estimation method by means of a computer, that are preferable in a case where an object is hydrogen (including light hydrogen, deuterium, and tritium) or a lithium, which has a small mass and whose quantum effect appears remarkably.
2. Description of Related Art
In recent years, attention has been focused on hydrogen as an alternative energy source to a fossil fuel such as oil in an attempt to deal with global environment problems such as ozone layer destruction and air pollution. A representative example of the use of hydrogen is a fuel cell, in which an easily oxidizable fuel such as hydrogen is reacted with oxygen rich in the atmosphere, and chemical energy generated through the chemical reaction is not converted into heat, but directly converted into electric energy. Further, when hydrogen is used as the fuel, a product of the reaction with oxygen is water alone, and hence there is in no danger of leading to environmental destruction, and hydrogen has thus been considered to serve as a mainstream energy in the future.
Incidentally, palladium, Pd is capable of absorbing hydrogen in large amount, whereas nickel, Ni generates hydride only at high pressure, and platinum, Pt just allows hydrogen to penetrate and is not capable of absorbing hydrogen in large amount. As thus described, since nickel, Ni, palladium, Pd and platinum, Pt have different hydrogen storage characteristics although all belonging to group 10 metal, it is necessary to consider a behavior of hydrogen as an adsorbed atom due to an inherent potential that is formed in accordance with each atom.
The potential is obtained in such a manner that an adsorbed atom is arranged on the surface, a total energy (excluding kinetic energy of the adsorbed atom) as a function of a coordinate of the atom is obtained by a first principle calculation based upon a density functional method (e.g. see “Physical Review”, issued on Nov. 9, 1964, Volume No. 136, p. 864-871 and “Physical Review”, issued on Nov. 15, 1965, Volume No. 140, p. 1133-1138), and a hypersurface of a potential energy for the atom on the surface (which is a curve, a curved surface or a hypersurface depending upon a dimension, but here, it is regarded as a hypersurface in the case of a two or larger dimensions) is derived. From the view point of classical mechanics, a coordinate of the atom corresponding to an energy minimum point of the derived potential curved surface is at the adsorption position, and a value, obtained by dividing a partial differential coefficient of second order by a mass of the atom on a coordinate in a specific direction around the energy minimum point, calculating a square root of the obtained value, and multiplying the square root by Dirac constant h/2π, provides vibrational energy.
However, when the atom has a small mass, the quantum effect appears remarkably, and the minimum point of the potential curved surface is not necessarily the adsorption position. Further, in the case of a metal surface, typically, a non-harmonic characteristic of the potential curved surface is distinguished, and when the non-harmonic characteristic of the potential curved surface is distinguished, the square root of the partial differential coefficient of second order is not proportional to the vibrational energy. Further, an effect of finite zero-point energy exists.
This is because, in the quantum world, a material has bilateral characteristics of a particle and a wave, and the wave characteristic is distinguished especially on a microscopic scale. Therefore, in order to accurately grasp the quantum state of the adsorbed atom, it is necessary to solve a Schrödinger equation [Formula (1)] so as to calculate a wave function Ψ. In Formula (1), “m” is a mass of an adsorbed atom, “h” is a Planck's constant (note: “h/2π” is a Dirac constant), “V” is a potential energy, and “Ej” is eigen energy (characteristic value), and an eigen wave function Ψj corresponds to each eigen value Ej.
                                                        {                                                -                                                                                    (                                                  h                                                      2                            ⁢                            f                            ⁢                                                          I                              ^                                                                                                      )                                            2                                                              2                      ⁢                      m                                                                      ⁢                                                                            ∇                      ⇀                                        2                                    ⁢                                      +                                          V                      ⁡                                              (                                                  x                          ,                          y                          ,                          z                                                )                                                                                                        }                        ⁢            f            ⁢                                                  ⁢                                          μ                j                            ⁡                              (                                  x                  ,                  y                  ,                  z                                )                                              =                                    E              j                        ⁢            f            ⁢                                                  ⁢                                          μ                j                            ⁡                              (                                  x                  ,                  y                  ,                  z                                )                                                    ,                            Formula        ⁢                                  ⁢                  (          1          )                                                  where          ⁢                                          ⁢                                    ∇              ⇀                        2                          =                              (                                                            ∂                  2                                                  ∂                                      x                    2                                                              +                                                ∂                  2                                                  ∂                                      y                    2                                                              +                                                ∂                  2                                                  ∂                                      z                    2                                                                        )                    .                                                
Since the quantum states of the atom that is adsorbed are decided in accordance with the potential V formed by the adsorbing material, for example when the interaction between the adsorbed atom and the adsorbing material is strong and a deep potential is formed, the adsorbed atom is adsorbed on the surface of the adsorbing material in its stable state, and is thus not easily desorbed from the adsorbing material. Hence it is considered essential for enhancement of the hydrogen storage technique to realize the technique for highly accurately estimating quantum states of an atom or a molecule that is adsorbed.